You sure can. I think there are a few threads on the topic on this site, but basically you can just take your bottling wand and insert it into your tap faucet (or picinic faucet). Purge most of the gas out of your keg to reduce foaming, and fill your bottle. When you pull your wand out, there will be some headspace, so it is important to remove the bottling wand from the faucet and then fill the bottle the rest of the way so that foam comes out of the top. That will remove most if not all oxygen from the bottle. Cap immediately. The bottle should stay carbed for weeks or even months.

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If you make sure the bottle is very cold, you can try, but you still wind up with a lot of foam. If you've got a picnic tap laying around, I'd suggest the BierMuncher Bottle Filler (BMBF). The link is also stickied in this forum. Basically you plug a racking cane into a picnic tap and turn down your PSI. Stick a stopper on the racking cane and it allows you to keep the bottle slightly pressurized while you fill and the cane lets you add the beer at the bottom of the bottle.

Make sure your bottles are cold and fill them so that foam is coming out the top. If you seal them on the foam, they shouldn't oxidize and should last just as long as any other beer (years). I've been doing this with a few swing top bottles since I never bottled and never purchased a capper, works great!